QUANTUM MECHANICS: Are There Quantum Jumps?  and On the Present Status of Quantum Mechanics

Can Nothing Cause Nonlocal Quantum Jumps?
View Description Hide DescriptionA paradox is discussed in which a photon can occupy one of two positions, ‘left’ or ‘right.’ Quantum mechanics allows the two possibilities—‘nothing left, photon right’ and ‘photon left, nothing right’—to be combined in a (coherent) superposition; or alternatively in an (incoherent) mixture, with similar terms, but no phase relation between them. As the phase relation is statistically significant, and can in principle be revealed experimentally, the two superposed possibilities must both be present in nature, together, for they somehow ‘communicate’ with one another through that relation. The eigenvalue +1 can be assigned to the presence of the photon on the right, −1 to its absence, to construct a measurable physical quantity, ‘photon‐right.’ Its expectation vanishes for the aforementioned superposition. If we look for the photon on the left and do not find it, it must be on the right. The superposition accordingly collapses to the term ‘nothing left, photon right,’ whose expectation for photon‐right jumps from zero to one right away. Only with a mixture could one ascribe the initial (vanishing) expectation to an ignorance which is then overcome once the photon is not found on the left. The issue is: what exactly happens on the left to cause the ontic (and not merely epistemic) jump on the right? Is it some mental event? Or is it nothing at all?

Dynamical reduction models and the energy conservation principle
View Description Hide DescriptionA common feature of dynamical reduction models is the violation of energy conservation principle which usually shows up as a constant increase in time of the energy of isolated systems. Anyway for typical values of the parameters of the models, such a violation is usually so weak that cannot be detected with present‐day technology. . Despite the reduction mechanism itself seems responsible for this behaviour, we show that this is not a intrinsic property of dynamical reduction models: we exhibit a collapse model such that the energy of isolated systems does not diverge for large times but reaches an asymptotic finite value. This result could be interesting in understanding how to work out relativistic extensions of dynamical reduction models.

From Pure Spinor Geometry to Quantum Mechanics
View Description Hide DescriptionIt is shown how pure spinors might play a fundamental role in building up a mathematical basis for quantum mechanics. First they are the elementary constituents of strings, in spaces with lorentzian signature, where they replace the concept of point‐event, when dealing with quantum physics. Therefore the corresponding quantum field theory results fundamentally non local. Furthermore, if the Cartan’s equations defining pure spinors are interpreted as equations of motion for fermions, or fermion multiplets, several complex phenomena in elementary particle physics find plain explanations, which derive from the corresponding Clifford’s algebras and the correlated division algebras. In particular the U(1) at the origin of charges appear evident in most equations for fermion doublets. This could explain the frequency in nature of charged‐neutral doublets. The geometry of pure spinors contemplate the existence of compact manifolds in momentum space (spheres) where problems of quantum dynamics might be mathematically formulated. One of these may be identified with that S _{3} in which V. Fock (1935) formulated and solved, with great geometrical evidence, the quantum problem of the H‐atom stationary states, setting also in evidence its SO(4) symmetry: a mathematical way to quantum physics which deserves to be further explored.

Einstein Podolsky Rosen correlations involving mesoscopic quantum systems
View Description Hide DescriptionWe investigate multiphoton states generated by high‐gain optical parametric amplification of a single injected photon, polarization encoded as a “qubit”. Two different experimental configurations were adopted in order to investigate two different quantum processes: the optimal universal quantum cloning and the optimal phase‐covariant cloning. The output states of the two apparatuses were found to show the quantum superposition property of mesoscopic multi‐photon assemblies and the entanglement characteristics of the “Schroedinger Cat State”. This work represents an experimental attempt to test several fundamental quantum processes in a mesoscopic, or macroscopic frameworks. As it is well known, this is indeed one of the most challenging endavours of modern science.

Sharp and Unsharp Descriptions of Physical Magnitudes in Finite Dimensional Quantum Mechanics
View Description Hide DescriptionGeneralized (i.e., positive operator valued) observables generated by a standard (i.e., projection valued) observable via suitable confidence functions are introduced in the context of finite dimensional Hilbert quantum mechanics. These generalized observables are considered as unsharp realizations of the unique physical magnitude associated to the standard realization.
We show a theorem about the “physical equivalence” (in the sense of equal probability distributions) of the two situations “sharp state — unsharp observable” and “unsharp state — sharp observable”; in particular, this equivalence is obtained by a partially defined nonlinear, isometric (nonunitary) operator.

Liouville equation and Markov chains: epistemological and ontological probabilities
View Description Hide DescriptionThe greatest difficulty of a probabilistic approach to the foundations of Statistical Mechanics lies in the fact that for a system ruled by classical or quantum mechanics a basic description exists, whose evolution is deterministic. For such a system any kind of irreversibility is impossible in principle. The probability used in this approach is epistemological. On the contrary for irreducible aperiodic Markov chains the invariant measure is reached with probability one whatever the initial conditions. Almost surely the uniform distributions, on which the equilibrium treatment of quantum and classical perfect gases is based, are reached when time goes by. The transition probability for binary collision, deduced by the Ehrenfest‐Brillouin model, points out an irreducible aperiodic Markov chain and thus an equilibrium distribution. This means that we are describing the temporal probabilistic evolution of the system. The probability involved in this evolution is ontological.

Noncontextuality in Quantum Measure Theory
View Description Hide DescriptionThe Clauser‐Horne‐Shimony‐Holt‐Bell inequalities are necessary conditions for a set of no‐signalling probabilities for two measurers each with two alternative experiments each with two possible outcomes to admit a joint probability distribution. An analogue of these inequalities in the context of quantum measure theory is presented. Talk given by Fay Dowker.

Holistic Quantum Computational Semantics and Gestalt‐Thinking
View Description Hide DescriptionHuman perception like thinking seems to be essentially synthetic. We never perceive an object by scanning it point by point. We instead form right away a Gestalt, i.e. a global idea of it. Rational activity, as well, seems to be essentially based on gestaltic patterns. Quantum computation has suggested a new holistic semantics, which makes essential use of the characteristic “holistic” features of the quantum‐theoretic formalism. In this framework, meanings are represented by quantum information quantities: systems of qubits or, more generally, mixtures of systems of qubits. The global meaning of a compound expression (which may correspond to an entangled state) determines the meanings of its parts, but generally not the other way around.

How to Derive the Hilbert‐Space Formulation of Quantum Mechanics From Purely Operational Axioms
View Description Hide DescriptionIn the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of physical experiment and assuming experimental accessibility and simplicity as specified by five simple Postulates. This accomplishes the program presented in form of conjectures in the previous paper. Pivotal roles are played by the local observability principle, which reconciles the holism of nonlocality with the reductionism of local observation, and by the postulated existence of informationally complete observables and of a symmetric faithful state. This last notion allows one to introduce an operational definition for the real version of the “adjoint”—i. e. the transposition—from which one can derive a real Hilbert‐space structure via either the Mackey‐Kakutani or the Gelfand‐Naimark‐Segal constructions. Here I analyze in detail only the Gelfand‐Naimark‐Segal construction, which leads to a real Hilbert space structure analogous to that of (classes of generally unbounded) selfadjoint operators in Quantum Mechanics. For finite dimensions, general dimensionality theorems that can be derived from a local observability principle, allow us to represent the elements of the real Hilbert space as operators over an underlying complex Hilbert space (see, however, a still open problem at the end of the paper). The route for the present operational axiomatization was suggested by novel ideas originated from Quantum Tomography.

The Message of the Quantum?
View Description Hide DescriptionWe criticize speculations to the effect that quantum mechanics is fundamentally about information. We do this by pointing out how unfounded such speculations in fact are. Our analysis focuses on the dubious claims of this kind recently made by Anton Zeilinger.

Continuous Wave Function Collapse in Quantum‐Electrodynamics?
View Description Hide DescriptionTime‐continuous wavefunction collapse mechanisms not restricted to markovian approximation have been found only a few years ago, and have left many issues open. The results apply formally to the standard relativistic quantum‐electrodynamics. I present a generalized Schrödinger equation driven by a certain complex stochastic field. The equation reproduces the exact dynamics of the interacting fermions in QED. The state of the fermions appears to collapse continuously, due to their interaction with the photonic degrees of freedom. Even the formal study is instructive for the foundations of quantum mechanics and of field theory as well.

Properties and Dispositions: Some Metaphysical Remarks on Quantum Ontology
View Description Hide DescriptionAfter some suggestions about how to clarify the confused metaphysical distinctions between dispositional and non‐dispositional or categorical properties, I review some of the main interpretations of QM in order to show that — with the relevant exception of Bohm’s minimalist interpretation — quantum ontology is irreducibly dispositional. Such an irreducible character of dispositions must be explained differently in different interpretations, but the reducibility of the contextual properties in the case of Bohmian mechanics is guaranteed by the fact that the positions of particles play the role of the categorical basis, a role that in other interpretations cannot be filled by anything else. In Bohr’s and Everett‐type interpretations, dispositionalism is instrumentalism in disguise.

Quantization as a dimensional reduction phenomenon
View Description Hide DescriptionClassical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three dimensional supermanifold. Quantization is then achieved by a process of dimensional reduction of this supermanifold. We prove that this procedure is equivalent to the well‐known method of geometric quantization.

Arrival time and backflow effect
View Description Hide DescriptionWe contrast the average arrival time at x according to the Bohmian mechanics of one dimensional free Schrödinger evolution with the standard quantum mechanical one. For positive momentum wave functions the first cannot be larger than the second one. Equality holds if and only if the wave function does not lead to position probability backflow through x. This position probability backflow has the least upper bound of approximately 0.04. We describe a numerical method to determine this backflow constant, introduced by Bracken and Melloy, more precisely and we illustrate the approximate wave function of maximal backflow.

Some Comments on the Formal Structure of Spontaneous Localization Theories
View Description Hide DescriptionWe propose a mathematical and a conceptual framework that encompasses and generalizes the “flash” ontology discussed in a recent paper by R. Tumulka.

On the statistics of quantum expectations for systems in thermal equilibrium
View Description Hide DescriptionThe recent remarkable developments in quantum optics, mesoscopic and cold atom physics have given reality to wave functions. It is then interesting to explore the consequences of assuming ensembles over the wave functions simply related to the canonical density matrix. In this note we analyze a previously introduced distribution over wave functions which naturally arises considering the Schrödinger equation as an infinite dimensional dynamical system. In particular, we discuss the low temperature fluctuations of the quantum expectations of coordinates and momenta for a particle in a double well potential. Our results may be of interest in the study of chiral molecules.

Quantum Abraham models with de Broglie‐Bohm laws of electron motion
View Description Hide DescriptionWe discuss a class of quantum Abraham models in which the N‐particle spinor wave function of N electrons solves a Pauli respectively Schrödinger equation, featuring regularized classical electromagnetic potentials which solve the semi‐relativistic Maxwell‐Lorentz equations for regularized point charges, which move according to some de Broglie‐Bohm law of quantum motion. Thus there is a feedback loop from the actual particle motions to the wave function. The electrons have a bare charge and positive bare mass different from their empirical charge and mass due to renormalization by the self‐fields. In the classical limit the various models reduce to the Hamilton‐Jacobi version of corresponding Abraham models of classical electron theory.

Macro‐objectivation: a challenge in quantum field theory
View Description Hide DescriptionThermodynamics of irreversible processes is taken as the phenomenological starting point for the description of macroscopic systems in quantum mechanics and state parameters, which are amenable to be attributed an objective meaning, are introduced inside non relativistic quantum field theory when the macroscopic system is locally at equilibrium. Conditions for these state parameters to obey a deterministic time evolution are indicated and discussed. The formalism is developed also considering the case of more component systems and bound states. The situation in which the deterministic dynamics of the state parameters breaks down is also envisaged and it is argued that in this case a stochastic generalisation of the theory is called for. First attempts in this direction are outlined, naturally leading to a rooting of the concept of microsystem inside both quantum theory and an objective phenomenological context.

Instantaneous and Local Nondemolition Measurement of Nonlocal Observables using Entangled States
View Description Hide DescriptionWith reference to a system of n spin‐1/2 particles which are distributed between two space‐like separated parties, we present two procedures to perform an instantaneous and local measurement of any nondegenerate observable having as its eigenstates the orthonormal basis of n‐partite entangled states introduced in [S. Bose, V. Vedral, and P. L. Knight, Phys. Rev. A 57, 822 (1998)], whose vectors reduce to the Bell states for n = 2 and to the GHZ states for n = 3. The first procedure implements a genuine nondemolition measurement by resorting to two n‐particle entangled states as an additional resource. The second one distinguishes between those eigenstates, though without preserving them (i.e., it is a demolition measurement), but it requires only a single couple of additional particles in a (maximally entangled) Bell state. Both methods are instantaneous, in the sense that the outcome of the measurement process is completely determined as soon as the local operations, whose duration can be made as short as one wishes, have been independently performed in the two distant regions where the particles are located.